Scattering diagrams were first introduced in the context of the Strominger-Yau-Zaslow approach to mirror symmetry [1]}, [2]}, and applied to DT invariants of quivers with potential in [3]}. More generally, as we explain in §REF , for a given triangulated category \(\mathcal {C}\)  and phaseThe scattering diagram \(\mathcal {D}_\psi \) 
is invariant under \((\psi ,\gamma ,Z)\mapsto (\psi +\pi ,-\gamma ,Z)\)  and \((-\psi ,\gamma ^\vee ,Z^\vee )\) 
where \(\gamma ^\vee \)  is the image of \(\gamma \)  under derived duality, and \(Z^\vee (\gamma ):=-\overline{Z(\gamma ^\vee )}\) . For most of this work
we restrict to the interval \((-\frac{\pi }{2},\frac{\pi }{2}]\) .
\(\psi \in {R}/2\pi {Z}\) ,
the scattering diagram \(\mathcal {D}_\psi \)  is supported on a set of real-codimension one loci (or active rays)
\(\mathcal {R}_\psi (\gamma )\)  in the space of stability conditions \(\operatorname{Stab}\mathcal {C}\)  where
the central charge has fixed argument \(\arg Z(\gamma )=\psi +\frac{\pi }{2}\)  and
supports semi-stable objects, in the sense that the rational DT index
\(\bar{\Omega }_Z(\gamma ) \sum _{m|\gamma } \frac{y-y^{-1}}{m(y^m-y^{-m})} \Omega _Z(\gamma /m)\vert _{y\rightarrow y^m}\) 
